Chi-square tests worksheet with answers

Free printable Chi-square tests worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
face123456observed252021152217

A die is rolled 120 times to test whether it is fair. The counts of each face are shown. Compute the chi-square goodness-of-fit statistic χ² for H₀: each face has probability 1/6.

n = 120k = 6
χ² =
2.Easy
colourredorangeyellowgreenblueobserved7233412628claimed30%20%20%15%15%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 200 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 200k = 5
χ² =
3.Medium
busbikecarTotalstudents6181640staff12303880Total184854120

The contingency table shows observed counts. Compute the chi-square statistic χ² for the test of independence between the row and column variables. Do not use a continuity correction.

N = 1202 × 3
χ² =
4.Medium
no defectminormajorTotalday shift15131038night shift10303676Total254346114

The contingency table shows observed counts. For a chi-square test of independence, find the expected count E for the cell “night shift, no defect”.

row total = 76column total = 25N = 114
E =
5.Hard

A chi-square goodness-of-fit test checks whether counts in 6 categories follow a Poisson distribution whose mean is estimated from the same data. How many degrees of freedom df does the test have?

k = 6
df =
6.Hard

A chi-square test of independence is carried out on a contingency table with 3 rows and 4 columns (not counting the totals). How many degrees of freedom df does the test have?

3 × 4
df =

Answer key

  1. 1. χ² = 3.2
  2. 2. χ² = 4.317
  3. 3. χ² = 0.7083
  4. 4. E = 16.67
  5. 5. df = 4
  6. 6. df = 6

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